Local Optima Networks of the Quadratic Assignment Problem

Abstract

Using a recently proposed model for combinatorial landscapes, Local Optima Networks (LON), we conduct a thorough analysis of two types of instances of the Quadratic Assignment Problem (QAP). This network model is a reduction of the landscape in which the nodes correspond to the local optima, and the edges account for the notion of adjacency between their basins of attraction. The model was inspired by the notion of 'inherent network' of potential energy surfaces proposed in physicalchemistry. The local optima networks extracted from the so called uniform and real-like QAP instances, show features clearly distinguishing these two types of instances. Apart from a clear confirmation that the search difficulty increases with the problem dimension, the analysis provides new confirming evidence explaining why the reallike instances are easier to solve exactly using heuristic search, while the uniform instances are easier to solve approximately. Although the local optima network model is still under development, we argue that it provides a novel view of combinatorial landscapes, opening up the possibilities for new analytical tools and understanding of problem difficulty in combinatorial optimization.

Local Optima Networks of the Permutation Flow-Shop Problem

“…Considering all instances, ρ is in the 95% confidence interval (0.78, 0.81), indicating that the higher the fitness of a LON N , the easier it is to reach it. This is consistent with results on other combinatorial spaces displaying a positive correlation between fitness and basin size [7].…”

ParadisEO-MO: from fitness landscape analysis to efficient local search algorithms

“…Finally, the ParadisEO-MO tools for fitness landscape analysis and local search algorithms have been validated on a large range of optimization problems from both academic and realworld fields, including vehicle routing (Lecron et al, 2010), scheduling (Marmion et al, 2011a,b), packing (Khanafer et al, 2010(Khanafer et al, , 2011, NK-landscapes , quadratic assignment problem (Daolio et al, 2010), and bio-informatics (Boisson et al, 2011), among many others.…”

Understanding Phase Transitions with Local Optima Networks: Number Partitioning as a Case Study

“…The parameter k was varied from 0.4 to 1.2 in steps of 0.1. For each landscape, we extract the full local optima network using code adapted from Daolio et al [31,32]. We then construct both the monotonic local optima networks (M-LON) and the compressed monotonic local optima networks (CM-LON).…”